Geodesic
Differential inclusions with unbounded right-hand side. Existence and relaxation theorems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 246-262 Cet article a éte moissonné depuis la source Math-Net.Ru

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A differential inclusion in which the values of the right-hand side are nonconvex closed possibly unbounded sets is considered in a finite-dimensional space. Existence theorems for solutions and a relaxation theorem are proved. Relaxation theorems for a differential inclusion with bounded right-hand side, as a rule, are proved under the Lipschitz condition. In our paper, in the proof of the relaxation theorem for the differential inclusion, we use the notion of $\rho-H$ Lipschitzness instead of the Lipschitzness of a multivalued mapping.
Keywords: unbounded differential inclusions, existence and relaxation theorems. 
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A. A. Tolstonogov. Differential inclusions with unbounded right-hand side. Existence and relaxation theorems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 246-262. http://geodesic.mathdoc.fr/item/TIMM_2014_20_3_a16/

[1] Wazewski T., “Sur une generalization des la notion de solution d'une equation au contingent”, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 10:1 (1962), 11–15 | MR | Zbl

[2] Filippov A. F., “Klassicheskie resheniya uravnenii s mnogoznachnoi pravoi chastyu”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1967, no. 3, 16–26 | Zbl

[3] Goncharov V. V., Tolstonogov A. A., “Sovmestnye nepreryvnye selektory mnogoznachnykh otobrazhenii s nevypuklymi znacheniyami i ikh prilozheniya”, Mat. sb., 182:7 (1991), 946–969 | MR | Zbl

[4] Loewen P. D., Rockafellar R. T., “Optimal control of unbounded differential inclusions”, SIAM J. Control Optim., 32:2 (1994), 442–470 | DOI | MR | Zbl

[5] Ioffe A., “Existence and relaxation theorems for unbounded differential inclusions”, J. Convex Anal., 13:2 (2006), 353–362 | MR | Zbl

[6] Himmelberg C. J., “Measurable relations”, Fund. Math., 87 (1975), 53–72 | MR | Zbl

[7] Tolstonogov A. A., “K teoreme Skortsa–Dragoni dlya mnogoznachnykh otobrazhenii s peremennoi oblastyu opredeleniya”, Mat. zametki, 48:5 (1990), 109–120 | MR | Zbl

[8] Attouch H., Wets R. J. B., “Quantitative stability of variational systems: I. The epigraphical distance”, Trans. Amer. Math. Soc., 328:2 (1991), 695–729 | MR | Zbl

[9] Gutman S., “Topological equavalence in the space of integral vector-valued functions”, Proc. Amer. Math. Soc., 93:1 (1985), 40–42 | DOI | MR | Zbl

[10] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1968, 272 pp. | MR